Are there scripts available to solve the unsteady vorticity transport equation in Matlab?

I want to reproduce results from an old code so I can test a new code. The old code solves the unsteady vorticity transport equation in 2D with a constant kinematic viscosity term. I'm interested in 2-D tank-like geometries with inlets and outlets. I want to solve problems where there are initially either one or two layers of fluid.

The problem seems straightforward enough that I expected to find codes/applets online, but so far I don't see anything. A Matlab script with plotting capabilities would be great, but I don't see anything like that at the file exchange. Maybe someone knows of another resource?